Operator mixing and three-point functions in N=4 SYM

TL;DR

This paper investigates three-point functions in N=4 SYM, emphasizing the importance of operator mixing at both weak and strong coupling to uphold superconformal symmetry constraints.

Contribution

It demonstrates the crucial role of operator mixing in three-point correlator computations at 1-loop and strong coupling, highlighting its necessity for symmetry preservation.

Findings

Operator mixing cancels symmetry-violating contributions at 1-loop.

Mixing between different impurity states is essential at strong coupling.

Some string interactions defy superconformal symmetry expectations.

Abstract

We study the three-point functions between two BPS and one non-BPS local gauge invariant operators in N=4 Super Yang-Mills theory. In particular we show, in explicit 1-loop examples, that the operator mixing discussed in arXiv:0810.0499 plays an important role in the computations of the correlators and is necessary to cancel contributions that would violate the constraints following from the superconformal and the bonus U(1)_Y symmetries. We analyse the same type of correlators also at strong coupling by using the BMN limit of the AdS_5xS^5 string theory. Again the mixing between states with different types of impurities is crucial to ensure the cancellation of various amplitudes that would violate the constraints mentioned above. However, on the string side, we also find some examples of interactions between one non-BPS and two BPS states that do not satisfy expectations based on the superconformal and the bonus U(1)_Y symmetries.